Question

the length and breadth of a rectangular park are in the ratio of 7:5.A2 m wide path is running all around outside of the park, the area of the path is 448m^2 find the length (1)length of the park (2)breadth of the park​

Answer 1

$\bf{\huge{\underline{\boxed{\rm{\red{Answer:}}}}}}$

Given:-

• the length and breadth of a rectangular park are in the ratio of 7:5

Let x be the common multiple of this ratio.

Length = 7x m

Breadth = 5x m

To find :-

• Area of the rectangular park

Area of the rectangular park = L × B

Area = (7x) (5x)

Area = 35x²

Given :-

• a 2 m wide path is running all around outside of the park
• the area of the path is 448m^2 find the length

To find :-

• Length of the park
• Breadth of the park

Solution:-

As mentioned in the question, "a 2 m wide path is running all around outside of the park" the length and breadth of the path = 2m, we can assume it to be in shape of a square.

Length of the park including the 2 m wide path,

Length = 7x + 2 + 2 = 7x + 4m

Breadth of the park including the 2 m wide path,

Breadth = 5x + 2 + 2= 5x + 4m

Now, let's calculate the area of the park including the dimensions of the path,

Area of the park = l × b

448 = (7x + 4 ) (5x + 4) - 35x²

448 = 7x (5x + 4) 4 (5x + 4) - 35x²

448 = 35x² + 28x + 20x + 16 -35x²

448 = 35x² + 48x + 16 - 35x²

448 = 48x + 16

448 - 16 = 48x

432 = 48x

48x = 432

x = $\bf\large\frac{432}{48}$

$\bf{\large{\underline{\boxed{\rm{\orange{<strong><u> </u></strong><strong><u> </u></strong><strong><u>x </u></strong><strong><u>=</u></strong><strong><u> </u></strong><strong><u>9</u></strong><strong><u> </u></strong><strong><u>cm</u></strong><strong><u> </u></strong>}}}}}}$

Substitute the value of x in the values of length and breadth.

$\bf{\large{\underline{\boxed{\rm{\pink{Length\:of\:the\:rectangle \:=\:7x\:=\:7\: × 9\:= 63m}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\red{Breadth\:of\:the\:rectangle \:=\:5x\:=5× 9\:=45m}}}}}}$

$\bf{\huge{\underline{\boxed{\rm{\green{Verification:}}}}}}$

We are mainly dealing with the dimensions of the rectangular park, so the verification is also for the same.

Given :-

• the length and breadth of a rectangular park are in the ratio of 7:5

Length = 63 m

Breadth = 45 m

Ratio = 7:5

Length : Breadth = 7:5

$\bf\large\frac{Length}{Breadth}$ = $\bf\large\frac{7}{5}$

$\bf\large\frac{63}{45}$ = $\bf\large\frac{7}{5}$

Dividing LHS by 9,

$\bf\large\frac{7}{5}$ = $\bf\large\frac{7}{5}$

LHS = RHS.

Hence answer is verified!

Answer 2

Step-by-step explanation:

length 63 cm. breadth 45 cm